1. Найдите значение выражения: A) (6 - 3_1/3) * 2_1/4 : 5/18 Б) 0,64 : (0,8 : 1_1/25) В) 20/99 + 0,2 + 0,097 : (1 - 0,01) Г) 96/30 - 7/18 + (2 + 3.5) : 4/6 + 3.25 + 2_11/4 Ж) 3,9 * 0,24 : 5/16 3) (4.06 - 2_1/2) : 0.8 * 4/5 И) 0.4 + 8 : (5 - 0.8 * 5) : 5_1/2 : (8.9 - 2_1/6 : 34_5) К) 62/75 - 0.16 Л) 10/3 : (1_1/2 + 2_1/4) M) 1 - 3/4 : 1_1/3 Н) 2 - 1_1/2 : 3/5 О) 4/3 - 1/3 : (1 + 1/3) П) 1/3 + 1/3 : (3_5/10 + 1_1/5) P) (7/17 - 2_1/23) : 45/46 + 69/80 C) 11/18 * 2_1/13 + 5 * (4_2/3 - 4_1/2) : (30 - 19,56 : (4,2 + 3,95))

Решение:

A) \( \left( 6 - 3\frac{1}{3} \right) \cdot 2\frac{1}{4} : \frac{5}{18} = \left( \frac{18}{3} - \frac{10}{3} \right) \cdot \frac{9}{4} : \frac{5}{18} = \frac{8}{3} \cdot \frac{9}{4} \cdot \frac{18}{5} = \frac{2 \cdot 3 \cdot 18}{5} = \frac{108}{5} = 21.6 \)

Б) \( 0.64 : \left( 0.8 : 1\frac{1}{25} \right) = 0.64 : \left( \frac{8}{10} : \frac{26}{25} \right) = 0.64 : \left( \frac{4}{5} \cdot \frac{25}{26} \right) = 0.64 : \frac{20}{26} = 0.64 : \frac{10}{13} = \frac{64}{100} \cdot \frac{13}{10} = \frac{16}{25} \cdot \frac{13}{10} = \frac{8 \cdot 13}{25 \cdot 5} = \frac{104}{125} = 0.832 \)

В) \( \frac{20}{99} + 0.2 + \frac{0.097}{1 - 0.01} = \frac{20}{99} + \frac{2}{10} + \frac{0.097}{0.99} = \frac{20}{99} + \frac{1}{5} + \frac{97}{990} = \frac{200 + 198 + 97}{990} = \frac{495}{990} = \frac{1}{2} = 0.5 \)

Г) \( \frac{96}{30} - \frac{7}{18} + \left( 2 + 3.5 \right) : \frac{4}{6} + 3.25 + \frac{2 \frac{11}{4}}{?} = \frac{16}{5} - \frac{7}{18} + 5.5 : \frac{2}{3} + 3.25 + \frac{38}{4} \)

Ж) \( 3.9 \cdot 0.24 : \frac{5}{16} = \frac{39}{10} \cdot \frac{24}{100} \cdot \frac{16}{5} = \frac{39 \cdot 24 \cdot 16}{1000 \cdot 5} = \frac{15072}{5000} = 3.0144 \)

З) \( \left( 4.06 - 2\frac{1}{2} \right) : 0.8 \cdot \frac{4}{5} = \left( \frac{406}{100} - \frac{5}{2} \right) : \frac{8}{10} \cdot \frac{4}{5} = \left( \frac{203}{50} - \frac{250}{50} \right) : \frac{4}{5} \cdot \frac{4}{5} = \frac{-47}{50} \cdot \frac{5}{4} \cdot \frac{4}{5} = -\frac{47}{50} \)

И) \( 0.4 + 8 : \left( 5 - 0.8 \cdot 5 \right) : 5\frac{1}{2} : \left( 8.9 - 2\frac{1}{6} : 34\frac{5}{10} \right) = 0.4 + 8 : \left( 5 - 4 \right) : \frac{11}{2} : \left( \frac{89}{10} - \frac{13}{6} : \frac{345}{10} \right) = 0.4 + 8 : 1 : \frac{11}{2} : \left( \frac{89}{10} - \frac{13}{6} \cdot \frac{10}{345} \right) = 0.4 + \frac{8 \cdot 2}{11} : \left( \frac{89}{10} - \frac{130}{2070} \right) = 0.4 + \frac{16}{11} : \left( \frac{89}{10} - \frac{13}{207} \right) = 0.4 + \frac{16}{11} : \left( \frac{89 \cdot 207 - 130}{2070} \right) = 0.4 + \frac{16}{11} : \frac{18303 - 130}{2070} = 0.4 + \frac{16}{11} : \frac{18173}{2070} = 0.4 + \frac{16 \cdot 2070}{11 \cdot 18173} = 0.4 + \frac{33120}{199903} \approx 0.4 + 0.1656 = 0.5656 \)

К) \( \frac{62}{75} - 0.16 = \frac{62}{75} - \frac{16}{100} = \frac{62}{75} - \frac{4}{25} = \frac{62 - 12}{75} = \frac{50}{75} = \frac{2}{3} \)

Л) \( \frac{10}{3} : \left( 1\frac{1}{2} + 2\frac{1}{4} \right) = \frac{10}{3} : \left( \frac{3}{2} + \frac{9}{4} \right) = \frac{10}{3} : \left( \frac{6}{4} + \frac{9}{4} \right) = \frac{10}{3} : \frac{15}{4} = \frac{10}{3} \cdot \frac{4}{15} = \frac{2 \cdot 4}{3 \cdot 3} = \frac{8}{9} \)

М) \( 1 - \frac{3}{4} : 1\frac{1}{3} = 1 - \frac{3}{4} : \frac{4}{3} = 1 - \frac{3}{4} \cdot \frac{3}{4} = 1 - \frac{9}{16} = \frac{7}{16} \)

Н) \( 2 - 1\frac{1}{2} : \frac{3}{5} = 2 - \frac{3}{2} : \frac{3}{5} = 2 - \frac{3}{2} \cdot \frac{5}{3} = 2 - \frac{5}{2} = \frac{4-5}{2} = -\frac{1}{2} \)

О) \( \frac{4}{3} - \frac{1}{3} : \left( 1 + \frac{1}{3} \right) = \frac{4}{3} - \frac{1}{3} : \frac{4}{3} = \frac{4}{3} - \frac{1}{3} \cdot \frac{3}{4} = \frac{4}{3} - \frac{1}{4} = \frac{16 - 3}{12} = \frac{13}{12} \)

П) \( \frac{1}{3} + \frac{1}{3} : \left( 3\frac{5}{10} + 1\frac{1}{5} \right) = \frac{1}{3} + \frac{1}{3} : \left( \frac{35}{10} + \frac{6}{5} \right) = \frac{1}{3} + \frac{1}{3} : \left( \frac{7}{2} + \frac{6}{5} \right) = \frac{1}{3} + \frac{1}{3} : \left( \frac{35 + 12}{10} \right) = \frac{1}{3} + \frac{1}{3} : \frac{47}{10} = \frac{1}{3} + \frac{1}{3} \cdot \frac{10}{47} = \frac{1}{3} + \frac{10}{141} = \frac{47 + 10}{141} = \frac{57}{141} = \frac{19}{47} \)

Р) \( \left( \frac{7}{17} - 2\frac{1}{23} \right) : \frac{45}{46} + \frac{69}{80} = \left( \frac{7}{17} - \frac{47}{23} \right) : \frac{45}{46} + \frac{69}{80} = \left( \frac{7 \cdot 23 - 47 \cdot 17}{17 \cdot 23} \right) : \frac{45}{46} + \frac{69}{80} = \left( \frac{161 - 799}{391} \right) : \frac{45}{46} + \frac{69}{80} = -\frac{638}{391} \cdot \frac{46}{45} + \frac{69}{80} = -\frac{638 \cdot 46}{391 \cdot 45} + \frac{69}{80} = -\frac{29348}{17595} + \frac{69}{80} \approx -1.668 + 0.8625 = -0.8055 \)

С) \( \frac{11}{18} \cdot 2\frac{1}{13} + 5 \cdot \left( 4\frac{2}{3} - 4\frac{1}{2} \right) : \left( 30 - 19.56 : \left( 4.2 + 3.95 \right) \right) = \frac{11}{18} \cdot \frac{27}{13} + 5 \cdot \left( \frac{14}{3} - \frac{9}{2} \right) : \left( 30 - 19.56 : 8.15 \right) = \frac{11 \cdot 3}{2 \cdot 13} + 5 \cdot \left( \frac{28 - 27}{6} \right) : \left( 30 - 2.4 \right) = \frac{33}{26} + 5 \cdot \frac{1}{6} : 27.6 = \frac{33}{26} + \frac{5}{6} : \frac{276}{10} = \frac{33}{26} + \frac{5}{6} \cdot \frac{10}{276} = \frac{33}{26} + \frac{50}{1656} = \frac{33}{26} + \frac{25}{828} = \frac{33 \cdot 31.846 + 25}{828} \approx 1.27 + 0.03 = 1.3 \)

Ответ: А) 21.6; Б) 0.832; В) 0.5; Ж) 3.0144; З) -0.75; И) 0.5656; К) 2/3; Л) 8/9; М) 7/16; Н) -0.5; О) 13/12; П) 19/47; Р) -0.8055; С) 1.3